【摘要】 提出用样条有限点法计算拱的横向振动和纵向振动的最小频率。用3次B样条函数的线性组合模拟拱自振时的位移振型函数,根据Hamilton原理推导出了拱结构自由振动频率方程。通过实例验证了样条有限点法计算效率高、精度高、计算格式简单,较有限元法具有很大优越性。计算分析了轴向变形对横向振动最小频率的影响,提出了临界矢跨比的概念。考虑轴向变形时不仅频率系数的大小发生了变化,同时它的变化规律也与原来不同。当结构的矢跨比小于临界矢跨比时,横向振动最小频率较不计轴向变形时减小,随着矢跨比的增大逐渐增大;当结构的矢跨比大于临界矢跨比时,横向振动最小频率较不计轴向变形时增大,随着矢跨比的增大逐渐减小。由此给出了目前广泛使用的横向振动最小频率曲线的适用范围,同时建立了纵向振动频率计算用曲线。更多还原

【Abstract】 A spline finite point method is presented for studying the natural frequency of arch structures.The displacement mode shape function of the arch free vibration is simulated with a linear combination of cubic B–spline.The free vibration frequency equation of arch structures is derived according to Hamilton principle.The spline finite point method is verified by examples.The results show that the method is efficient and accurate.This method is better than finite element method.The influence of the axial deformation on the natural frequency is analyzed.The concept of the critical rise span ratio is put forward.Not only the value of the frequency coefficient is changed,but also its variation law is considered.When the arch rise span ratio is less than the critical rise-span,the axial deformation makes the natural frequency decrease.The lateral frequency coefficient increases as the rise span ratio increases.When the arch rise span ratio is greater than the critical rise-span,the axial deformation makes the natural frequency increase.The lateral frequency coefficient decreases as the rise span ratio increases.更多还原